面向均值-方差投资组合优化的基于KKT重构的决策聚焦学习
Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation
- University of Tsukuba（筑波大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对均值-方差投资组合优化中预测与决策目标不一致的问题，提出基于KKT条件的单层决策聚焦学习公式，显式保留约束，在真实ETF数据上取得最优投资表现。
AI中文摘要：
均值-方差投资组合优化（MVO）是数据驱动资产管理中的核心框架。一种广泛采用的方法是两阶段框架，即首先预测预期收益，然后基于这些预测求解优化问题，其中预测模型通过最小化预测误差来训练。然而，这种预测目标与下游投资组合决策的质量并不一致。决策聚焦学习（DFL）直接在训练过程中最小化下游决策损失，因此成为一个有前景的方向。然而，现有的用于MVO的DFL方法依赖替代损失或约束松弛来保证可解性，这导致预测模型训练与评估时求解的受约束MVO之间存在结构性不匹配。我们提出了一种单层优化公式，将下层MVO的Karush-Kuhn-Tucker（KKT）最优性条件纳入上层学习问题。该公式显式保留了预算约束和卖空约束，同时仍可被标准非线性优化求解器高效求解。在两个具有不同相关结构的资产池的真实ETF（交易所交易基金）数据上进行的滚动窗口实验表明，我们的方法在多个投资指标上取得了最佳性能，并且由于所提出的正则化而展现出性能提升。
英文摘要：
Mean-variance portfolio optimization (MVO) is a central framework in data-driven asset management. A widely adopted approach is a two-stage framework that first predicts expected returns and then solves the optimization problem based on these predictions, with the predictive models trained by minimizing prediction errors. However, this objective of prediction is not aligned with the quality of the downstream portfolio decision. Decision-focused learning (DFL), which directly minimizes the downstream decision loss within the learning process, has thus emerged as a promising direction. However, existing DFL approaches to MVO rely on surrogate losses or constraint relaxations for tractability, creating a structural mismatch between predictive model training and the constrained MVO solved at evaluation. We propose a single-level optimization formulation that incorporates the Karush-Kuhn-Tucker (KKT) optimality conditions of the lower-level MVO into the upper-level learning problem. This formulation explicitly preserves the budget and short-sale constraints while remaining tractable for standard nonlinear optimization solvers. Rolling-window experiments on real-world ETF (Exchange Traded Funds) data across two asset universes with different correlation structures show that our method achieved the best performance on multiple investment metrics and also demonstrated performance improvement due to the proposed regularization.
